Finite Group Databasebeta

← C151×#8914 #50313839

Subgroups — C151×#8914 #50313839

Order 38656.

468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2379×C151C211yesmaximal, characteristic
2#1959×C151C211yesmaximal, characteristic
3#1836×C151C212yesmaximal, complemented
4C2×#329×C151C211yesmaximal, characteristic
5#1295×C151C212yesmaximal, complemented
6C2×#124×C151C2211yescharacteristic
7C2×#103×C151—21no—
8C2×#102×C151—21no—
9C2×#97×C151C2211yescharacteristic
10C2×#97×C151C2212yes—
11#391×C151—21no—
12#388×C151—22no—
13#386×C151—21no—
14#385×C151—22no—
15#384×C151C2211yescharacteristic
16#382×C151C2212yes—
17#340×C151—22no—
18#340×C151—22no—
19#329×C151C414yescomplemented
20C22×Q8×C151D411yescharacteristic
21C22×D4×C151D411yescharacteristic
22C23×C4×C151—21no—
23C22×C8×C151—22no—
24C22×C8×C151—21no—
25#124×C151—22no—
26#124×C151C2×C412yes—
27#124×C151Q812yes—
28C2×C4⋊C4×C151—22no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151D412yes—
32C2×C4⋊C4×C151D412yes—
33C2×C22⋊C4×C151—22no—
34C2×C22⋊C4×C151—22no—
35C2×C22⋊C4×C151—21no—
36C2×C42×C151—21no—
37C2×C42×C151C2311yescharacteristic
38#103×C151—42no—
39#102×C151—42no—
40#97×C151—22no—
41#97×C151—22no—
42#97×C151C2×C414yescomplemented
43#95×C151—22no—
44#95×C151—22no—
45#95×C151—22no—
46C24×C151—21no—
47C2×Q8×C151—21no—
48C2×Q8×C151—41no—
49C2×Q8×C151—41no—
50C2×Q8×C151C4⋊C412yes—
51C2×D4×C151—21no—
52C2×D4×C151—41no—
53C2×D4×C151—41no—
54C2×D4×C151C4⋊C412yes—
55C22×C4×C151—21no—
56C22×C4×C151—22no—
57C22×C4×C151—22no—
58C22×C4×C151—41no—
59C22×C4×C151—81no—
60C22×C4×C151—82no—
61C22×C4×C151C2×D411yescharacteristic
62C22×C4×C151C2×D412yes—
63C2×C8×C151—22no—
64C2×C8×C151—24no—
65C2×C8×C151—42no—
66C2×C8×C151—41no—
67C2×C8×C151—42no—
68C2×C8×C151—41no—
69C4⋊C4×C151—42no—
70C4⋊C4×C151—42no—
71C4⋊C4×C151—41no—
72C4⋊C4×C151—41no—
73C4⋊C4×C151—44no—
74C4⋊C4×C151—81no—
75C22⋊C4×C151—24no—
76C22⋊C4×C151—24no—
77C22⋊C4×C151—81no—
78C22⋊C4×C151—82no—
79C42×C151—81no—
80C42×C151C22×C411yescharacteristic
81C42×C151C2×Q811yescharacteristic
82C42×C151#4112yes—
83C23×C151—22no—
84C23×C151—41no—
85C23×C151—42no—
86C23×C151—42no—
87C23×C151—41no—
88C23×C151#12011yescharacteristic
89Q8×C151—42no—
90Q8×C151—81no—
91D4×C151—42no—
92D4×C151—81no—
93C2×C4×C151—21no—
94C2×C4×C151—22no—
95C2×C4×C151—21no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151—41no—
99C2×C4×C151—41no—
100C2×C4×C151—42no—
101C2×C4×C151—42no—
102C2×C4×C151—42no—
103C2×C4×C151—42no—
104C2×C4×C151—42no—
105C2×C4×C151—42no—
106C2×C4×C151—84no—
107C2×C4×C151—81no—
108C2×C4×C151—82no—
109C2×C4×C151C2×C4⋊C411yescharacteristic
110C2×C4×C151C4×D412yes—
111C2×C4×C151C22⋊Q812yes—
112C2×C4×C151#12311yescharacteristic
113C8×C151—42no—
114C8×C151—44no—
115C22×C151—42no—
116C22×C151—44no—
117C22×C151—81no—
118C22×C151—81no—
119C22×C151—82no—
120C22×C151#38511yescharacteristic
121C22×C151#45311yescharacteristic
122C22×C151#45412yes—
123C22×C151#45511yescharacteristic
124C22×C151#45512yes—
125C4×C151—21no—
126C4×C151—21no—
127C4×C151—22no—
128C4×C151—22no—
129C4×C151—42no—
130C4×C151—82no—
131C4×C151—82no—
132C4×C151—161no—
133C2×C151—82no—
134C2×C151#165711yescharacteristic
135C2×C151#165911yescharacteristic
136C2×C151#166212yes—
137C2×C151#185611yescharacteristic
138C2×C151#186012yes—
139#8914C15111yesmaximal, characteristic, direct product factor, Sylow
140C151#891411yescharacteristic, direct product factor, Sylow
141#2379C2×C15111yescharacteristic
142#1959C2×C15111yescharacteristic
143#1836C2×C15112yescomplemented
144C2×#329C2×C15111yescharacteristic
145#1295C2×C15112yescomplemented
146C2×#124C22×C15111yescharacteristic
147C2×#103—21no—
148C2×#102—21no—
149C2×#97C22×C15111yescharacteristic
150C2×#97C22×C15112yes—
151#391—21no—
152#388—22no—
153#386—21no—
154#385—22no—
155#384C22×C15111yescharacteristic
156#382C22×C15112yes—
157#340—22no—
158#340—22no—
159#329C4×C15114yescomplemented
160C22×Q8D4×C15111yescharacteristic
161C22×D4D4×C15111yescharacteristic
162C23×C4—21no—
163C22×C8—22no—
164C22×C8—21no—
165#124—22no—
166#124C2×C4×C15112yes—
167#124Q8×C15112yes—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4D4×C15112yes—
172C2×C4⋊C4D4×C15112yes—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—21no—
176C2×C42—21no—
177C2×C42C23×C15111yescharacteristic
178#103—42no—
179#102—42no—
180#97—22no—
181#97—22no—
182#97C2×C4×C15114yescomplemented
183#95—22no—
184#95—22no—
185#95—22no—
186C24—21no—
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8C4⋊C4×C15112yes—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C4⋊C4×C15112yes—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—41no—
199C22×C4—81no—
200C22×C4—82no—
201C22×C4C2×D4×C15111yescharacteristic
202C22×C4C2×D4×C15112yes—
203C2×C8—22no—
204C2×C8—24no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—41no—
208C2×C8—41no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—44no—
214C4⋊C4—81no—
215C22⋊C4—24no—
216C22⋊C4—24no—
217C22⋊C4—81no—
218C22⋊C4—82no—
219C42—81no—
220C42C22×C4×C15111yescharacteristic
221C42C2×Q8×C15111yescharacteristic
222C42#41×C15112yes—
223C23—22no—
224C23—41no—
225C23—42no—
226C23—42no—
227C23—41no—
228C23#120×C15111yescharacteristic
229Q8—42no—
230Q8—81no—
231D4—42no—
232D4—81no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—84no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4C2×C4⋊C4×C15111yescharacteristic
250C2×C4C4×D4×C15112yes—
251C2×C4C22⋊Q8×C15112yes—
252C2×C4#123×C15111yescharacteristic
253C8—42no—
254C8—44no—
255C22—42no—
256C22—44no—
257C22—81no—
258C22—81no—
259C22—82no—
260C22#385×C15111yescharacteristic
261C22#453×C15111yescharacteristic
262C22#454×C15112yes—
263C22#455×C15111yescharacteristic
264C22#455×C15112yes—
265C4—21no—
266C4—21no—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—82no—
271C4—82no—
272C4—161no—
273C2—82no—
274C2#1657×C15111yescharacteristic
275C2#1659×C15111yescharacteristic
276C2#1662×C15112yes—
277C2#1856×C15111yescharacteristic
278C2#1860×C15112yes—
subgroupG/H
center, socleC23×C151#120
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #1836×C151C2semidirect
5. #1295×C151C2semidirect
19. #329×C151C4semidirect
42. #97×C151C2×C4semidirect
139. #8914C151direct (N × H)
140. C151#8914direct (N × H)
143. #1836C2×C151semidirect
145. #1295C2×C151semidirect
159. #329C4×C151semidirect
182. #97C2×C4×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#2379×C1512
#1959×C1512
#1836×C1512
C2×#329×C1512
#1295×C1512
#8914151